This is an experiential study of investigating a consistent method for deriving the correlation between sentence vector and semantic meaning of a sentence. We first used three state-of-the-art word/sentence embedding ...
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The work of Christoforou and Tzavaras (Arch Rat Mech Anal 229(1):1–52, 2018, [5]) on the extension of the relative entropy identity to the class of hyperbolic-parabolic systems whose hyperbolic part is symmetrizable ...
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An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating the expected rank of an induced map o...
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The symmetric energy-conserved splitting FDTD scheme developed in[1]is a very new and efficient scheme for computing theMaxwell’s *** is based on splitting the whole Maxwell’s equations and matching the x-direction ...
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The symmetric energy-conserved splitting FDTD scheme developed in[1]is a very new and efficient scheme for computing theMaxwell’s *** is based on splitting the whole Maxwell’s equations and matching the x-direction and y-direction electric fields associated to the magnetic field *** this paper,we make further study on the scheme for the 2D Maxwell’s equations with the PEC boundary *** new energy-conserved identities of the symmetric EC-S-FDTD scheme in the discrete H^(1)-norm are *** is then proved that the scheme is unconditionally stable in the discrete H^(1)-*** the new energy-conserved identities,the super-convergence of the symmetric EC-S-FDTD scheme is further proved that it is of second order convergence in both time and space steps in the discrete H^(1)-*** experiments are carried out and confirm our theoretical results.
Various methods can obtain certified estimates for roots of polynomials. Many applications in science and engineering additionally utilize the value of functions evaluated at roots. For example, critical values are ob...
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This paper considers algebraic ordinary differential equations(AODEs)and study their polynomial and rational *** authors first prove a sufficient condition for the existence of a bound on the degree of the possible po...
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This paper considers algebraic ordinary differential equations(AODEs)and study their polynomial and rational *** authors first prove a sufficient condition for the existence of a bound on the degree of the possible polynomial solutions to an *** AODE satisfying this condition is called *** the authors prove that some common classes of low-order AODEs are *** rational solutions,the authors determine a class of AODEs,which are called maximally comparable,such that the possible poles of any rational solutions are recognizable from their *** generalizes the well-known fact that any pole of rational solutions to a linear ODE is contained in the set of zeros of its leading ***,the authors develop an algorithm to compute all rational solutions of certain maximally comparable AODEs,which is applicable to 78.54%of the AODEs in Kamke's collection of standard differential equations.
The mobility of members of a species, which may be modelled by diffusion, plays an important role in biology, though much remains to be discovered concerning its effects. It is therefore relevant to ask how diffusion ...
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In any organization, the capability, knowledge and skills play a significant role in success of an employee. For instant, in hospital management, the performance evaluation of an employee is mainly based on qualitativ...
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This paper concerns the propagation of high frequency wave-beams in highly turbulent atmospheres. Using a paraxial model of wave propagation, we show in the long-distance weak-coupling regime that the wavefields are a...
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MSC Codes 35B20, 35B27, 35B35, 35B40, 47A53A central property of (Chern) topological insulators is the presence of robust asymmetric transport along interfaces separating two-dimensional insulating materials in differ...
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